Internal problem ID [15232]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.2 Homogeneous differential equations with
constant coefficients. Exercises page 121
Problem number: 442.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+10*diff(y(x),x$2)+12*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (c_{1} +c_{2} x +c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 32
DSolve[y''''[x]+4*y'''[x]+10*y''[x]+12*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} (c_4 x+c_2 \cos (2 x)+c_1 \sin (2 x)+c_3) \]